论文标题
限制随机化的特性，对实验设计的影响
Properties of restricted randomization with implications for experimental design
论文作者
论文摘要
最近，人们对使用严格限制的随机化设计产生了越来越多的兴趣，在随机对照试验中，在观察到的协变量上实现平衡。但是，当限制严格时，治疗效应估计器的均值均方根误差会有很高的风险。在本文中，我们正式化了这种风险，并提出了一种基于组合的新方法来描述和解决这个问题。首先，我们通过重新提供完全随机化和限制随机化的一些已知属性来验证我们的新方法。其次，我们为受限设计提出了一种新颖的诊断措施，该方法仅使用设计组合中的信息。第三，我们表明在随机实验中，均值估计器的平均平方误差的方差是该诊断度量的线性函数。最后，我们确定限制设计可能会导致出现高平方错误的风险增加的情况，并讨论如何使用我们的诊断措施来检测此类设计。我们的结果对任何受限制的随机设计具有影响，可用于评估观察到的协变量和避免过于限制性设计的平衡之间的权衡。
Recently, there as been an increasing interest in the use of heavily restricted randomization designs which enforces balance on observed covariates in randomized controlled trials. However, when restrictions are strict, there is a risk that the treatment effect estimator will have a very high mean squared error. In this paper, we formalize this risk and propose a novel combinatoric-based approach to describe and address this issue. First, we validate our new approach by re-proving some known properties of complete randomization and restricted randomization. Second, we propose a novel diagnostic measure for restricted designs that only use the information embedded in the combinatorics of the design. Third, we show that the variance of the mean squared error of the difference-in-means estimator in a randomized experiment is a linear function of this diagnostic measure. Finally, we identify situations in which restricted designs can lead to an increased risk of getting a high mean squared error and discuss how our diagnostic measure can be used to detect such designs. Our results have implications for any restricted randomization design and can be used to evaluate the trade-off between enforcing balance on observed covariates and avoiding too restrictive designs.
